Problem: Find an explicit formula for the arithmetic sequence $-5,13,31,49,...$. Note: the first term should be $\textit{b(1)}$. $b(n)=$
The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${-5}$ and the common difference is ${18}$. ${+18\,\curvearrowright}$ ${+18\,\curvearrowright}$ ${+18\,\curvearrowright}$ ${-5},$ $13,$ $31,$ $49,...$ This is the explicit formula for the arithmetic sequence $-5,13,31,49,...$. $b(n)={-5}+{18}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.